As is known, computer simulation refers to representing a certain event on a computer in a simulated manner. The expression “representation of an event” as used herein refers to visually or statistically expressing changes over time in the state of existing or unknown matter that causes the event. The computer simulation uses a mathematical model that represents an event in an abstract form. The mathematical model is a collection of elements correlated by predetermined mathematical expressions. The computer simulation is performed with a simulation program, such as simulation software or a simulator, executed by a computer.
An electromagnetic field simulator represents, on a computer, a state of electromagnetic fields in a space inside or outside a physical object, such as a printed circuit board, a wireless communication circuit, a high-frequency circuit, an antenna, a radar device, a radio-wave absorber, a power system, or photonic crystal. Specifically, the state of electromagnetic fields is represented by determining the strengths of electromagnetic fields in a mathematical model, i.e., in individual elements, each time a time-step is increased by one in a given time span and then performing processing for displaying animation and so on based on the determined strengths. The strengths of the electric fields of the elements are determined using Maxwell's equations. As the number of elements increases, a larger amount of time is required to determine the strengths of the electromagnetic fields.
One example of the electromagnetic field simulator is an FDTD (finite-difference time-domain) simulator. The FDTD simulator employs an FDTD method to represent, on a computer, the state of an electromagnetic field in space inside or outside of a physical object as described above. The “FDTD method” as used herein refers to a method in which points at which electric field strengths are to be calculated and points at which magnetic field strengths are to be calculated are discretely placed in virtual space (analysis space) in which the shape of a physical object is defined and the electric field strengths and the magnetic field strengths are alternately calculated along a time axis. Hereinafter, the points at which electric field strengths are calculated are referred to as “electric-field calculation points” and the points at which magnetic field strengths are calculated are referred to as “magnetic-field calculation points”.
More specifically, in the FDTD method, multiple rectangular-parallelepiped cells are set in virtual space. Each cell is given a medium-dependent electric constant of a medium (an object or air) occupying a large area of the cell. Examples of the electric constant include an electric permittivity, a magnetic permeability, and an electrical conductivity. The electric-field calculation points are arranged at the centers of the edges of each cell and the magnetic-field calculation points are arranged at the centers of the faces of each cell. In such a manner, in the FDTD method, the electric-field calculation points and the magnetic-field calculation points are discretely placed. Placing the electric-field calculation points and the magnetic-field calculation points in virtual space is referred to as “spatial discretization”.
In the FDTD method, when the position of a wave source, the magnitude of the wave source, and the time-step size are specified, electric field strengths at the electric-field calculation points and magnetic field strengths at the magnetic-field calculation points are repeatedly determined in a given time span. More specifically, the electric-field strength at one electric-field calculation point is determined based on an electric-field strength determined one time step earlier at the same electric-field calculation point and magnetic-field strengths determined a half time step earlier at the magnetic-field calculation points adjacent to the electric-field calculation point. Similarly, the magnetic-field strength at one magnetic-field calculation point is determined based on a magnetic-field strength determined one time step earlier at the same magnetic-field calculation point and electric field strengths determined a half time step earlier at the electric-field calculation points adjacent to the magnetic-field calculation point. The method for alternately determining the electric field strengths and the magnetic field strengths every half time step is called the “leapfrog algorithm”.
A multilayer printed circuit board has conductive layers and dielectric layers. Each conductive layer includes conductors and insulators at which a two-dimensional circuit pattern is formed. Each dielectric layer includes an insulator. In the multilayer printed circuit board, the conductive layers and the dielectric layers are alternately provided in the thickness direction. The dielectric layer further includes vias, which are conductors for interconnecting the conductors in particular conductive layers or interconnecting the conductors in all conductive layers. The above-described FDTD simulator is also used to design such a type of multiplayer printed circuit board. The multilayer printed circuit board has a larger number of conductive layers than a single-layer printed circuit board. Thus, for discretization of virtual space in which the shape of a multilayer printed circuit board is defined, the FDTD simulator sets a vast number of cells, compared to the single-layer printed circuit board.
The existing FDTD simulator sets cells so that edges of each circuit wire and edges of the cells agree with each other in a plane parallel to the printed circuit board. Thus, the contour shape of each wire is precisely traced by edges of the cells. For example, as illustrated in FIG. 25, there is a case in which two rectangular circuit wires 61 and 62 that are parallel to each other are arranged so that they are spaced apart from each other in their lateral direction and overlap each other slightly in their longitudinal direction. In this case, by setting narrow cells having the width of the overlapping portion, the existing FDTD simulator allows the same electric constant as that of the two circuit wires 61 and 62 to be given to cell groups 66 and 67 having the same shape and the same size as the two wires 61 and 62.
That is, the existing FDTD simulator is adapted to set narrow cells in order to achieve the tracing described above. This arrangement, however, has a problem. Specifically, when the density of the circuit pattern increases, the number of cells increases and the amount of time for computing the electromagnetic-field strengths increases.
As defined by the so-called “Courant-Friedrichs-Lewy condition”, the upper limit of the time-step size is proportional to a minimum cell size. Thus, when narrow cells are set for the tracing described above, the time-step size also needs to be reduced. This leads to an increase in the number of time steps, and thus there is a problem in that the amount of time for computing the electromagnetic-field strengths increases.
In addition, during determination of the positions of the edges of the cells, the existing FDTD simulator performs processing for detecting edges of circuit wires. Thus, when the circuit pattern has a high density, a large amount of time is required for processing for spatial discretization.